Device and method for generating a targeted realistic motion of particles along shortest paths with respect to arbitrary distance weightings for simulations of flows of people and objects

ABSTRACT

A system for controlling motions of a plurality of particles in a spatial area with at least one target and at least one obstacle, has a first detection device for detecting positions of the particles at a starting time; predicting a future path search of the particles occurs by way of a computer device, wherein the region has been superimposed by a cell grid and each cell takes on various occupation and total potential states, and each cell is associated with a target potential determining how particles are attracted to a target, and is associated with an obstacle potential determining how particles are repelled by an obstacle, and wherein each particle is associated with a particle potential, wherein a total potential in a cell is made up of the values of the target potential and the obstacle potential in the cell and the particle potentials of particles in cells adjacent to the cell, and particles each change from a cell into an adjacent cell having a least total potential, and additionally, starting from a target to each cell, the target potential for each cell is calculated using a length of the shortest distance from the cell to each cell center point. A central controller controls the motions of the particles in case of forecast critical situations.

Device and method for generating a targeted realistic motion ofparticles along shortest paths with respect to arbitrary distanceweightings for simulations of flows of people and objects

The present invention relates to a system and a method for controllingmotions of a multiplicity of particles in a spatial region comprising atleast one target and at least one obstacle.

Mass-typical phenomena occur at any place where people gather en-masse.Some of these phenomena may be life-threatening, for example if panicbreaks out at a mass event. Further phenomena require suitable steeringmeasures so as to control events effectively.

Devices for reproducing flows of people imitate the behavior of a largenumber of people at different mass events, for example during theOktoberfest beer festival, in particular for statistical purposes and soas to improve safety at the location. One objective for example is theidentification of critical masses with the aid of the simulation, thatis to say the identification of risks caused by concentrations of peopleand critical flows of people as well as a prediction regarding thetemporal progression thereof so as to be able to introduce suitablemeasures.

A device for simulating a flow of people calculates the next position ofa person, in terms of time and space, on the basis of mathematicalmethods and thus on the basis of set provisions which are intended tomimic the human behavior pattern. Different models from the field ofmicro- and macromodeling are used, more specifically methods based onpartial differential equations through to methods based on cellularautomata.

According to the prior art, these approaches are already provided tosimulate flows of people in particular. However, these conventionalapproaches do have shortcomings, which limit an accurate reproduction ofmass phenomena and thus the usability of simulation results.

A frequently selected approach for simulating flows of people is that ofmethods based on cellular state automata [1]. A region, for example astreet of houses, is superimposed by a cell grid. Hexagonal grids areselected for example. Square or triangular cells are just as common.Each cell may take on different states, for example filled with anobstacle, or occupied by a person, or empty. Such states are updatedover the course of time by rule sets or automata. Cells may also containtargets which people aspire to reach. Cells may also contain sourcesfrom where people originate. The following sub-models and theirinteraction form the basic ideas of this automaton:

-   -   a target model determines how objects/people move towards a        target.    -   a model of object or person motion determines how objects/people        behave towards one another.    -   an obstacle model defines how objects, people and obstacles        move.

The value of an approach which mimics mechanisms known from the physicsof electronics is now proven. This is implemented by potential fields inthe mathematical formulation.

Targets attract objects or people, just like a positive charge attractselectrons. The strength of the potential field is determined in theprior art as a function of the Euclidean distance between the person orobject and the target. For this approach, an unobstructed view isnecessary, so that people do not get caught on obstacles. Alternatively,a flooding method is thus used in the prior art, in which the number ofcells to be covered is counted around obstacles starting from the targetto the person. The potential is determined as a function of the numberof cells between the target and the person.

Objects or people repel one another, just like electrons repel eachother. The strength of the potential field is conventionally determinedas a function of the Euclidean distance between the people or objects.

Obstacles repel objects or people, just like a negative charge repelselectrons. The strength of the potential field is conventionallydetermined as a function of the Euclidean distance between the person orobject and the obstacle.

A key problem when modeling flows of objects and people is the pathsearch to the target. If an unobstructed view to the target is possible,the finding of the target is trivial. Objects and people move directlytowards the target, possibly with small deviations. However, if animpenetrable obstacle is located between the people and the target, itis not easy to determine the direction of travel. For example, in thecase of a U-shaped obstacle, open towards the people, in front of thetarget, the strategy to move directly towards the target would result inpeople becoming trapped in the obstacle.

Complex methods for path searching are necessary in all forms of methodsfor simulating flows of objects and people in which there are obstacles.These methods are intended to provide a path to the target and also atthe same time to consider realistic human behavior. Realistic humanbehavior includes, inter alia, the selection of the shortest paths andan avoidance of certain areas. For example, roads are avoided and, wherenecessary, are crossed merely in an almost perpendicular direction.

The device proposed in this instance enables such a realistic pathsearch. Many problems of conventional methods, which in many casesdemonstrate unrealistic behavior of the flows of people and objects, areavoided. In particular, the proposed device makes it possible toimplement a certain intelligence of the particles, which are consideredfor example to represent pedestrians. It is thus possible to form anaversion to a specific territory, for example the avoidance of roads ordense crowds. Such territories are basically only entered if they cannotbe avoided, for example if a target is on another side of the road. Thepath over this territory is kept as short as possible. For example, thisis shown in FIG. 7 a. Such a realistic behavior is significant inparticular if the open spaces to be considered are large and theexpected density of people is low. For example, this concerns anoptimization of the design of shopping centers or the consideration ofcomplex spaces, partly covered by buildings.

A much more realistic approach compared to conventional devices isprovided. Conventional devices and methods sometimes demonstrate veryunrealistic behavior of people and objects. The device proposed in thisinstance leads to a significant increase in validity with use ofsimulations of flows of objects and people, with only a minimallyincreased computational effort.

Numerous methods for the target finding of flows of people can be foundin the literature. These can be divided into two approaches: graph-basedpath searches and path searches on the basis of potentials or metrics.

Graph-based path searching solves the problem of view obstruction byintroducing orientation points. At least one orientation point, whichcan be controlled, is to be visible from each place in the simulationarea. If at least one orientation point is to be visible from each placein the simulation area, this means that a direct connection of twoorientation points is not disturbed by an obstacle. Upon reaching theorientation point, a further orientation point will, at the latest, bevisible and may serve as the next orientation point. The exact pointwhen a change in orientation point should take place is an open problem.However, the results of corresponding simulations of flows of objectsand people depend significantly and critically on this decision. Allorientation points together, including the actual target, form a graphso that the search for a path is reduced to the problem of finding apath in a graph. The main drawback of this method is the fixation onindividual structures, the orientation points and edges, which in manycases leads to an unrealistic behavior of the people and objects. Theintroduction of an intelligent path selection on the basis of preferredterritories is thus only possible to a very limited extent.

A second alternative is path searching on the basis of potentials ormetrics. This path searching method, which above all is used in cellularautomata, involves the fixation on individual structures. Starting fromthe target, a value is assigned to each point in the space. The valuesincrease with distance from the target. This spatial assignment orfunction is referred to as a potential or metric. If all other effectsin simulations of flows of objects and people, such as behavior towardsone another and behavior when negotiating obstacles or random effectsare disregarded when establishing the motion method, the motion methodis reduced to a movement towards the minimum of the potential thusdetermined. The potential values of the selected path increase with timeuntil the person has finally reached the potential minimum, since allother typical behaviors implemented in current simulators of flows ofobjects and people, such as repulsion of other people and of obstacles,can also be modeled by means of potential, and path searching on thebasis of the potential minimum can also be retained with considerationof other effects.

Generally, as is the case for example with an unobstructed view, acorresponding potential function can only be provided with difficulty asan analytical function, that is to say a function which can be providedexplicitly. In the case of an unobstructed view, the Euclidean distancefor example is a suitable potential function. In the case of a blockedview, the potential function has to be calculated in the simulationitself, which necessitates a discretization for potential calculation,even with a continuous and thus grid-independent approach. In allconventional simulators of flows of objects and people, in order tocalculate the target potential, the minimum number of moves required tothe target along the discretization directions is taken as a basis forpotential, or a version scaled with a constant parameter. The potentialsare calculated using “Dijkstra's algorithm”. When using a rectangulargrid this approach corresponds substantially to the “1-metric” or“Manhattan metric”. This is shown in FIG. 1.

On the one hand, Dijkstra's approach is not fixed to individualpredefined structures, but on the other hand the approach provides anunrealistically large number of possibilities of motion. This is shownin FIG. 1. This leads to an unclear and unrealistic behavior of theflows of object and people, as shown in FIG. 6 a. This even leads insome cases to the freezing of the people in the simulations. It isnecessary to correct the potential approach. If the view to the targetis unobstructed, such a correction is quite simple. However, if anobstacle has to be navigated, there is no possibility for correction incurrent simulators. The next cell is selected randomly or heuristicallyfrom the cells with the lowest potential. Furthermore, the selectedpaths are generally longer than the shortest direct path owing to thediscrete number of directions. Similarly with regard to motion speed, acorrection with the objective of more realistic walking times for givendistances is necessary.

A reliable and, at the same time, simple method for realistic pathsearching in simulations of flows of objects and people is thus lacking.

The object of the present invention is to control motions of amultiplicity of particles, in particular people, in a spatial regioncomprising at least one target and at least one obstacle. A device orsystem for modeling particle flows is to realistically reproduce a pathsearch to the target, wherein in particular an obstacle is formedbetween the particles and the target. A path to the target is to beprovided and a realistic particle is to be considered, for example aselection of the shortest path or a preference for or avoidance ofspecific areas, in particular in the case of large open spaces to beconsidered and low expected particle densities. The validity ofsimulations of flows of people is to be significantly increased and acomputational effort is to be increased merely to a minimal extent.

The object is achieved by a device and a system according to the mainclaim and by a method according to the co-ordinated claim.

According to a first aspect, a system for controlling motions of aplurality of particles in a spatial region comprising at least onetarget and at least one obstacle is provided. The system ischaracterized by

-   -   detecting positions of the particles by means of a first        detection device at a starting time;    -   predicting a future path search of the particles by means of a        computer device, wherein the region has been superimposed by a        cell grid and each cell takes on various occupation and total        potential states, and each cell is assigned a target potential        determining how particles are attracted to a target, and an        obstacle potential is assigned determining how particles are        repelled by an obstacle, and wherein each particle is assigned a        particle potential, wherein a total potential in a cell is made        up of the values of the target potential and the obstacle        potential in the cell and the particle potentials of particles        in cells adjacent to the cell, and particles each change from a        cell into an adjacent cell having a least total potential, and        additionally, starting from a target to each cell, the target        potential for each cell has been calculated using a length of a        shortest distance from the target to a respective cell centre        point;    -   controlling the motions of the particles in case of forecast        critical situations by means of a central controller.

In this case particles are people in particular. The computer device maybe a simulation device, which uses particles which in particular consistof a metal. Such particles may be considered in the simulation device tobe representative of people. People with vehicles or animals are alsoincluded as particles by the present invention.

For example, a detection device is a sensor, in particular a camera or anoise detector.

A starting time is any desired moment in time at which a spatialarrangement of the particles is determined.

Critical situations are all situations which make it necessary tocontrol particle motions. For example, such situations may be a pullingin of a train, an overshoot of a particle density over a defined value,or a possible outbreak of panic.

The path search may be calculated both by spatially continuous orgrid-free approaches and by discrete or grid-based approaches, forexample as is the case with cellular state automata. The path search isthus compatible with all conventional modeling approaches. Inparticular, no modification is required in terms of other interactions,such as particle repulsion. Conventional modeling in current flows ofobjects and particles sometimes require merely minor modifications.

Compared to Dijkstra's algorithm, which is used conventionally, thecomputer device or simulation device requires merely a slightly greatercomputational effort, but at the same time exhibits a significantly morerealistic behavior of the particle flows or flows of people and objects.According to Dijkstra's algorithm, a complexity N, wherein N is thenumber of discretization points or cells, is to be expected. Accordingto the device according to the invention, a complexity lies at N LOG(N).

Starting from the target, in each point or discretization point, forexample the cell centre point of the cellular state automaton, thepotential with the shortest distance of the point to the target, that isto say the length of the shortest path, is initialized.

Each particle (or person or object) locally determines the direction ofthe shortest path to the target with the aid of an approximation of thegradient of the potential, that is to say the direction of the greatestchange in the potential. Each person moves in the direction of theshortest path in the case of a deterministic motion and with a disregardof all further effects.

As has already been mentioned above, the present invention isfurthermore based on the idea of establishing the direction of theshortest path by calculating the gradients of the previously determinedpotential, more specifically, the greatest change. The direction of theshortest path can thus be determined in each cell. Even in the case ofview-obstructing obstacles, the information of the direct and shortestpath to the target is thus provided.

The simulation device according to the invention can thus generally alsobe implemented without the above-described corrections with regard tomotion directions and speeds. If merely the type of calculation oftarget potential is exchanged in the conventional simulators of flows ofobjects and people, much better motion patterns are thus producedcompared to use of the conventional Dijkstra's algorithm. For example,much fewer bottlenecks occur at corners of obstacles. At the same time,only a minimal modification of the simulators provided is necessary.Generally, merely the function for potential calculation has to bereplaced.

In accordance with the present device, the actual direction of travel isdetermined by means of approximated gradients or directions of thestrongest potential change, wherein any approximations are possible, forexample methods of higher order.

Furthermore, a realistic calibration of essential parameters, inparticular in cellular approaches, is possible by the approach accordingto the invention with realistic motion patterns. This is a key point forcommercial applications. Furthermore, the simulation device allows abetter observance of guidelines for simulators of flows of people thanksto the graphic, more realistic modeling.

According to a second aspect, a method for controlling motions of amultiplicity of particles in a spatial region comprising at least onetarget and at least one obstacle is provided. The method ischaracterized by the following steps:

-   -   detecting positions of the particles at a starting time;    -   predicting a future path search of the particles, wherein the        region has been superimposed by a cell grid and each cell takes        on various occupation and total potential states, and each cell        is assigned a target potential determining how particles are        attracted to a target, and an obstacle potential is assigned        determining how particles are repelled by an obstacle, and        wherein each particle is assigned a particle potential, wherein        a total potential in a cell is made up of the values of the        target potential and the obstacle potential in the cell and the        particle potentials of particles in cells adjacent to the cell,        and particles each change from a cell into an adjacent cell        having a least total potential, and additionally, starting from        a target to each cell, the target potential for each cell has        been calculated using a length of a shortest distance from the        target to a respective cell centre point;    -   controlling the motions of the particles in case of forecast        critical situations.

Further advantageous embodiments are claimed in conjunction with thedependent claims.

According to an advantageous embodiment, the target potential can becalculated by means of the computer device by forming the target as acurve g of any shape and considering a propagation of a wave frontstarting from the target, wherein a propagation speed F (x, y) isselected at right angles to the wave front, and by assigning a futuretime T (x, y) of the wave front for each point (x, y) in the space,wherein the future time T (x, y) is the target potential.

Initialization or Calculation of the Potential.

The aim is to initialize each cell of the device/of a cellular stateautomaton with the shortest distance from its cell centre point (x, y)to the target, that is to say the length of the shortest path. If thetarget consists merely of a cell of the cellular state automaton, thepossibly weighted distance to the cell centre point of the target isused as a basis. If the target consists of a plurality of cells, thedistance to the polygon provided by the centre point of the outer cellsof a target is considered for example. In the most general case however,the target may also be considered as a curve g of any shape, thedistance to which is to be calculated.

A fundamental idea of the approach presented here is, instead ofcalculating the shortest distances, to alternatively consider thepropagation of a wave front starting from the target. At the moment intime t=0, the wave front is located on the outer edge of the target,that is to say the curve g. The wave front propagates at a predefinedspeed F (x, y) at right angles to the front, that is to say in a normaldirection. In the case of obstacles, F(x, y)=0 is true for thepropagation speed since these obstacles cannot be penetrated by thewave. The future time T(x, y) of the wave is now assigned to each point(x, y) in the space. T(x, y)=0 applies for points within the target, andT(x, y)=∞ applies for points which cannot be reached, for example pointsin obstacles.

If F(x, y)=1 applies for all points (x, y) which do not lie in anobstacle, the future time thus corresponds precisely to the Euclideanlength of the shortest path. The future times thus correspond to thesought potential, and the potential thus calculated, which correspondsto the actual distances, that is to say the Euclidean distances, will bereferred to hereinafter as the Euclidean potential, in contrast to the“Manhattan potentials”, which are based on a 1-metric/Manhattan metric,that is to say a calculation of distance along the axes of symmetry ofthe cellular automata. This corresponds to a Manhattan metric or1-metric.

An essential feature of a device according to the invention is thecalculation of potential for target determination by means of futuretimes of wave fronts starting from the target. A known fast-marchingmethod is used in simulations of flows of objects and people toeffectively determine the development of the wave fronts and to thuscalculate the potentials which are used for path searching.

According to a further advantageous embodiment, the propagation of thewave front can be described mathematically by an eikonal equation:

F(x,y)²·[(δ_(x) T(x,y))²′+(δ_(y) T(x,y))²]=1  Equation 1

The propagation of the wave can be described mathematically by theeikonal equation:

F(x,y)²·[(δ_(x) T(x,y))²′+(δ_(y) T(x,y))²]=1

where T(x, y)=0 for (x, y) over g, wherein ∂_(x, y) are the partialderivatives with respect to the location. In the proposed approach, theshortest distances and future times are thus determined based on thesolution of a partial differential equation: the eikonal equation.

Similarly to the potentials, a more explicit expression for the futuretime T(x, y), that is to say an explicit solution of the eikonalequation, cannot generally be provided. A numerical solution of theeikonal equation is necessary. An effective option is provided by theknown fast-marching method. Based on the grid provided by the centrepoints of the hexagonal cells of the state automata, the solution of theeikonal equation, that is to say the future times, is approximated. TheEuclidean or closest described weighted distances are thus alsoapproximated. The distances thus obtained form the target potential,which is used for target finding.

According to a further advantageous embodiment, a distance weighting,which is location-dependent, can be performed by selecting thepropagation speed F(x, y), wherein the propagation speed F(x, y) isinversely proportional to the distance weighting.

The target finding developed in accordance with the invention allows apath search by means of a potential approach with consideration ofarbitrary metrics, that is to say with arbitrary distance weightings,for example depending on the territory. In particular, a path searchbased on actual distances, that is to say the Euclidean metric, ispossible. With use of the developed device, the flows of objects andpeople or particles demonstrate realistic motion behavior. If all otherinfluences are ignored, for example random events and avoidance of otherrepulsions of people by obstacles, the shortest path to the target isselected with regard to the underlying metric. The people follow thegeodetic lines. With use of the actual distance weighting of theEuclidean metric, these are the straight lines if the view to the targetis unobstructed. However, the approach developed in accordance with thisinvention also allows the implementation of artificial intelligence bymeans of different weighting of distances by means of use of arbitrarymetrics. For example, it is thus possible to avoid specific territories.

An arbitrary distance weighting (metric) can be used as a basis, that isto say paths over a specific territory or paths through groups of peopleare provided with a greater distance than the Euclidean distance. Thismakes it possible to represent the avoidance of specific territories.

If an alternative F(x, y)>0 is selected, the specific future times andtherefore the distances, wherein future times always correspond todistances in the approach according to the invention, thus correspond toanother weighting of the distances, that is to say any metric other thanthe natural weighting, that is to say the Euclidean metric.

Weighting of the Distances; Selection of the Metric.

A location-dependent weighting of distances is possible by acorresponding selection of the propagation speed F(x, y). If a smallerpropagation speed is selected in specific areas, the wave thuspropagates there more slowly. Points in the corresponding areas arereached later, since the wave covers shorter distances in the sameperiod of time. Distances in these regions are thus weighted moreheavily. The shortest paths generally try to avoid these areas andtherefore the people and objects also avoid these areas since they movein the direction of the shortest path and thus follow this path. Thedirection of the shortest path in each point can be determined in eachcase by determining the gradient, that is to say the direction of thegreatest change in potential (see section below for determining thedirection of the shortest path or the section on motion methods).

If a person were to move in the direction of the greatest change inpotential at a locally different speed F(x, y), that is to say atprecisely the wave propagation speed, he would reach the target morequickly than on all other paths. Generally however, the speed of theperson does not correspond to the propagation speed of the wave F(x, y),even though both can vary locally at the same time. The propagationspeed of the wave F(x, y) is merely an auxiliary quantity in thiscontext and is inversely proportional to the weighting of the distances,that is to say the metrics. It does not coincide with the actual speedof particles (objects or people). For example, a person thus movesapproximately just as fast over grass and paved surfaces. Generallyhowever, the person would try to avoid the grass, and thereforedistances over this would be weighted more heavily. This would imply aslower propagation speed F(x, y) of the wave propagation in order todetermine the wave future time or the potential T(x, y). The actualspeeds of the person would not be variable however, and would beconstant in all areas. F(x, y) thus does not coincide with the speed ofthe person, but merely with the preference for specific territories orother conditions.

Owing to the selection of a corresponding propagation speed F(x, y), itis possible to implement a partly artificial intelligence of the objectsand people. Specific territories or specific regions are avoided by thepeople and objects.

Potentials for determining the target are calculated by means of futuretimes of wave fronts starting from the target by solving the eikonalequation. Distances can be attributed to future times, which makes itpossible to implement arbitrary distance weightings (metrics), inparticular the Euclidean metric, that is to say the actual metric.

Different assessment of preferred or unpreferred territories bydifferent weighting of the distances or different metrics allows apartly artificial intelligence of the people and objects, since thesemove along the geodetic lines, that is to say the shortest paths witharbitrary spatially variable distance weighting.

The device makes it possible to advantageously effectively implementshortest paths with respect to arbitrary metrics or arbitrary weightingsof the distances in the simulations of flows of objects and people. Inparticular in the case of potential-based cellular state automata, thecomputational effort is merely minimally greater, more specifically NLOG(N) instead of N, where N is the number of discretization points, forexample the number of cells, without additional storage requirement. Thepaths are thus reproduced much more realistically, since a certainintelligence of the pedestrians is enabled by a different weighting ofthe distances. It is thus possible to implement preferences for specificterritories, for example the avoidance of roads, via the distanceweighting. Such territories are then basically only entered if thiscannot be avoided, for example if a target is on the other side of theroad, and the path over this territory is kept as short as possible.

Furthermore, the device according to the invention advantageously allowsactual travel times of people to be approximated as accurately aspossible. Merely the discretization accuracies of the fast-marchingmethod are restrictive. This correction is detached from potential. Forexample, it may also be applied with a direct view, since the Euclideandistances can be determined directly in this instance.

According to a further advantageous embodiment, the computer device canlocally calculate the direction of the maximum change in magnitude ofthe target potential as the direction of the shortest path to thetarget, and based on this information can approximate a realistic motionalong the shortest path over the cell grid by means of a directioncorrection.

Motion Methods.

When using simulators of objects and people which are based on discretespatial structures, for example in the case of cellular automata, thedirection of motion cannot be selected arbitrarily. The motion along thedirection of motion predefined by the discretization may lead tounrealistic motion patterns and also to unrealistic motion times oraverage speeds. The path along the predefined direction is longer thanthe direct shortest path. Even when using potentials building on thedevices presented in this invention, corrections are necessary.

In conventional potential-based motion methods, in each step therespective adjacent cell with the smallest potential starting from thecurrent position is selected (method of zero order), and with randompath searches the adjacent cell is allocated a greater probability. Evenwhen using these conventional motion methods in combination with themethods implemented in this invention for calculating the underlyingpotentials for the purpose of target finding, much better results areobtained than with use of the Manhattan potentials used in currentsimulators of flows of people and objects, which are based on anunrealistic metric. The latter lead primarily to a multiplicity ofpossible paths. However, if merely the local potential minimums areconsidered, deviations from an ideal path are sometimes just as largewith use of the methods developed here for calculating potentials.

According to a further advantageous embodiment, starting from the targetpotentials of three cell centre points, the direction of the change inmagnitude of the target potential can be determined locally by means ofthe computer device by means of interpolation for each point of atriangle formed by the three cell centre points.

However, according to the numerical solution of the eikonal equation,the values for the future times or the potential are provided merely inthe grid points of the underlying grid. That is to say in the cellcentre points in accordance with the present device. By means ofinterpolation however, the gradient can also be obtained using thedevice presented here. An area is spanned locally by linearinterpolation of points of a triangle P0, P1 and P2, which area passesthrough the three points. With the aid of this area, the gradient ordirection of the strongest change can be determined locally in eachpoint of the triangle formed by P0, P1 and P2. The solution proposed byway of example in this instance corresponds to an interpolation of firstorder, that is to say the potential for determining the gradient. Anyother approaches for the approximate determination of the gradient arepossible however. In principle, any number of values and grid points canbe consulted in the approach developed in this instance in order todetermine the local direction of the strongest change by means ofinterpolation.

In the approach for path searching proposed in accordance with thedevice according to the invention however, the direction of the shortestpath to the target can be determined in each cell, as illustratedpreviously. This corresponds to a method of first or higher order. Theinformation regarding the direction of the shortest path can be used tocorrect the conventional approach. A better approximation of theshortest path or a motion along said path is thus enabled. Thiscorresponds to a method of higher order. In the corrections newlydeveloped in this instance, the path of the individual people can beselected in such a way that there is hardly any deviation from theoptimal path in spite of the restriction of the directions of motion bythe discrete structure of the cellular state automata. Deviations aregenerally unavoidable owing to the possibilities for motion limited bythe grid.

Motion Methods; Direction Correction

In the case of a grid-based device, for example with cellular automata,a free movement to the ideal position in the direction of the target isnot generally possible. A realistic movement along the shortest pathover the grid is approximated with the aid of correction mechanisms onthe basis of the information of the direction of the shortest path.

A path search is carried out with use of the local direction of theshortest path or the direction of the greatest change in potential. Thismeans that the conventional motion method is corrected based on thedirection information, even if the view of the target is obstructed.

According to a further advantageous embodiment, a consideration of anadjacent cell with a smallest target potential value and additionallytwo adjacent cells to the left and right of the adjacent cell with thesmallest target potential value may take place for direction correctionstarting from a current cell. Starting from the local direction of theshortest path of a cell centre point of the current cell, a normaldeviation nΔ can be established for these three adjacent cells at rightangles to the direction of the shortest path, wherein a normal deviationnΔ comprises a direction-dependent sign in each case. In addition, thesum NΔ of all normal deviations nΔ may be established from the previoussteps of an actual particle. The adjacent cells acting as the next cellfor the particle can be selected in such a way that the absolute valueof the sum NΔ of all previous steps of the particle, including thenormal deviation nΔ, is minimal, wherein the direction correction mayoccur as a result of the selection.

According to a further advantageous embodiment, if the selected adjacentcell is not the adjacent cell with the smallest target potential value,the target potential of the selected adjacent cell is decreased by meansof the control device until it is less than the smallest targetpotential value.

Motion Methods; Speed Correction

According to a further advantageous embodiment, a speed correction for amomentary particle speed may take place by means of the known previousdeviation from a shortest path.

Furthermore, correction factors for the momentary speed are determinedby means of the known previous deviations from an ideal path so as tothus ensure predefined average speeds of the simulated person for anypaths, even in the case of grid-based methods.

According to a further advantageous embodiment, a direction of a changein magnitude of the target potential may locally determine the directionof the shortest path to the target, wherein, for speed correctionstarting from the local direction of the shortest path of a cell centrepoint of a current cell, a tangential deviation tΔ in the direction ofthe shortest path can be established for any step for each cell which isentered next from the current cell. Furthermore, the sum TΔ of alltangential deviations tΔ of all previous steps of a current particle canbe established. An additional step for the particle can be granted bymeans of the control device if the sum TΔ of all tangential deviationstΔ of all previous steps for the particle is greater than an integralmultiple of a cell centre point distance, wherein an effective speed ofthe particle is thus increased locally in terms of time and is thereforecorrected.

The tangential deviations tΔ calculated in each step can be used tocorrect speed. If the sum of all deviations tΔ of all previous steps ofthis person exceeds an integral multiple of the grid distance, theperson will thus be granted an additional step. The effective speed ofthe person is increased locally in terms of time. This correctionsallows effective speeds, which approximate the expected journey timesfor a given path much better than without correction or with use ofknown corrections.

In the advantageous memory-saving implementation of the device accordingto the invention, merely the sum of all deviations nΔ as well as the sumof all deviations tΔ have to be stored. In each time step, thecorresponding current deviations nΔ and tΔ are added together afterselection of the move. Owing to the minimal number of variables to becalculated, the device according to the invention is also advantageousin terms of computational intensity.

According to a further advantageous embodiment, the sum NΔ of the normaldeviations or the sum TΔ of the tangential deviation may be set to 0 bymeans of the computer device if the particle is pushed too far from itsoriginal path or if the particle cannot freely select its path.

The correction method considered by way of example takes into accountthe sums of all deviations NΔ and tΔ in the past of each person or eachparticle. Alternative approaches are also possible. If the person orparticle is pushed too far from their original path, for example byinteraction with other particles or if the particle finds itself in asituation in which the path cannot actually be freely selected, forexample in the case of a dense crowd of particles, it is appropriate toreinitialize the sums of all deviations, that is to say to set to 0.

Enhancements

With regard to the above-presented corrections of the conventionalmotion method of an advantageous implementation for simulations of flowsof objects and people, there was a restriction to the current directionof the shortest path to the target. Information regarding the greatestchange in the potential however, that is to say the direction of theshortest path, offers a large number of alternative correction optionscompared to the above-presented implementations. For example, a currentshortest path can be determined by a weighted averaging of the optimalpaths or shortest paths in the past, that is to say the gradients in theprevious counts. In this regard, the deviations nΔ and t_(Δ) would thenbe selected. A summation of the previous deviations n_(Δ) would not benecessary; it would be suffice to take into account the currentdeviation n_(Δ) when considering a potential correction.

According to a further advantageous embodiment, a direction of a changein magnitude of the target potential, that is to say the direction ofthe shortest path to the target, can be determined locally by means ofthe computer device and a current shortest path for the particle can bedetermined by means of a weighted averaging of a change in the magnitudeof the target potential of the shortest path of a particle in previouscells.

According to a further advantageous embodiment, a path selection of theparticles may be random-based and the computer device may calculateprobabilities of individual cells on the basis of the total potentialand the information regarding the direction of the shortest path. Inother words, the above device is not limited to a deterministic pathsearch. An extension to random-based path selection is also possible. Inthe latter case, the corresponding probabilities of the individual cellswould not only be calculated on the basis of the potential, but alsobased on the information provided regarding the direction of theshortest path. A correction of the above-presented correction based ondeviations from the optimal direction is also possible.

According to a further advantageous embodiment, the central controllercan control building elements.

According to a further advantageous embodiment, building elements may bedoors, windows, signs, loudspeakers, lifts, escalators and/or lights.

The present invention will be described in greater detail on the basisof exemplary embodiments in conjunction with the drawings, in which:

FIG. 1 shows two exemplary embodiments of conventional cell grids of adevice according to the invention;

FIG. 2 shows two exemplary embodiments of a propagation of a wave frontstarting from a target;

FIG. 3 shows a hexagonal cell grid with an approximated Euclideanpotential;

FIG. 4 is a view of the average speed as a function of the direction oftravel and the motion correction;

FIG. 5 is a schematic view of the generation of a motion of particlesaccording to the invention by means of the simulation device accordingto the invention;

FIG. 6 shows a comparison of conventional path determination and pathdetermination according to the present invention;

FIG. 7 shows two exemplary embodiments of motions with differentdistance weightings;

FIG. 8 shows an exemplary embodiment of a simulation device according tothe invention; and

FIG. 9 shows an exemplary embodiment of a method according to theinvention.

FIG. 1 shows two exemplary embodiments of conventional cell grids for adevice according to the invention. FIG. 1 a shows a cell grid withsquare cells. FIG. 1 b shows a cell grid with hexagonal cells. In allconventional simulators of flows of objects and people, to calculate thetarget potential the minimum number of moves required to the targetalong the discretization directions is used as a basis for potential, ora version scaled with a constant parameter. The potentials arecalculated using “Dijkstra's algorithm”. When using a square grid, thisapproach basically corresponds to the “1-metric” or “Manhattan metric”.Possible paths MW are simply hatched. These possible paths MW areproduced with use of a potential-based path search based on Dijkstra'salgorithm or the Manhattan metric. Without specific potential correctionor path selection mechanisms, a multiplicity of possible paths of equallength is provided both for square and hexagonal grids. S denotes astarting cell. Z denotes a target cell. The Dijkstra approach is notlimited to individual predefined structures, but the approach providesan unrealistically high number, of possibilities of motion. This leadsto an unclear and unrealistic behavior of the flows or objects andpeople.

An advantageous implementation of a device according to the invention asa cellular state automaton with an underlying hexagonal grid will beelaborated hereinafter by way of explanation. For improvedunderstanding, a purely deterministic path search will be assumed.Furthermore, only an individual person will be considered, whose path isdetermined deterministically merely by the target potential.Interactions with other people or particles will not be considered. Acorresponding extension to this, as is to be found in most conventionalsimulations of flows of objects and people, is uncomplicated and easilypossible. Interactions with other particles and obstacle objects can beimplemented in all simulations of flows of objects and people byadditional potentials which are added to the target potentials.

The considered cellular state automaton consists of a regular grid withhexagonal cells (shown in FIG. 1 b), over which the considered objectsor particles move in discrete time steps. As described before, apotential is assigned to each cell. In FIG. 1 there is a “Manhattanpotential”. A cell may or may not be occupied either by a person orparticle. The particles each move in discrete time steps to the nextcell, wherein the direction of motion is determined by the potential ofthe adjacent cells, as will be explained hereinafter. If more than oneparticle or person is considered, the path determination also depends onthose particles or people located in the adjacent cell, but this will bedisregarded in the following consideration. As mentioned previously, anextension of the proposed device is possible without difficulty.

The device according to the invention for path determination carries outfour main sub-steps: the initialization or calculation of the potential,the weighting of the distances and selection of the metric, thedetermination of the direction of the shortest path, and the actualmotion with which a direction correction and/or speed correction isundertaken.

The device has been illustrated by way of example for a cellular stateautomaton with a regular hexagonal grid. In this case, thediscretization of the cellular state automaton and the discretizationused for numerical solution of an eikonal equation coincide with oneanother. However, a concordance of the grid is not necessary. Ageneralization of the method for any, in particular irregular grid ispossible, since effective methods for solving an eikonal equation areknown in the literature. In particular, it is even expedient to solvethe eikonal equation on a much more approximate grid so as to keep thecomputational effort for initializing the potential as low as possible.Local gradients for determining direction are also provided in thiscase. The described method can thus be used for all known cellular stateautomata as well as continuous simulations of objects and people. In thelatter case however, the correction step is superfluous since particlesand people can move freely.

FIG. 2 shows two embodiments of a propagation of a wave front startingfrom a target. FIG. 2 a shows a propagation of a wave front with speedF(x, y)=1. FIG. 2 b shows the propagation of a wave front with a speedF(x, y)>0 which is not constant over space. The device according to theinvention carries out the following steps: starting from the target, ineach point or discretization point, which for example are the cellcentre point of the cellular state automata, the potential with theshortest distance to the target, that is to say the length of theshortest path, is initialized. An arbitrary distance weighting (metric)can be used as a basis, that is to say paths over specific territoriesor paths through groups of people are allocated a greater distance thanthe Euclidean distance. This makes it possible to avoid certainterritories.

FIG. 2 is a schematic view of the propagation of a wave front a) withconstant propagation speed F(x, y) at right angles to the front, and b)with variable propagation speed F(x, y) at right angles to the front. Inb) the propagation speed is much lower in the left lower corner than inthe rest of the space. The fronts of the wave at specific times areshown in each case, more specifically as thin lines, and the path withthe shortest distance, which is illustrated as a dark line, from x=(x,y) to the target is shown, given by the curve g.

A fundamental idea of the present invention is, instead of calculatingthe shortest distances, to alternatively consider the propagation of awave front starting from the target. At the moment in time t=0, that isto say the start of the method, the wave front is located on the outeredge of the target, that is to say of the curve g. The wave frontpropagates at a predefined speed F (x, y) at right angles to the front,that is to say in normal direction. In the case of obstacles, F(x, y)=0is true for the propagation speed since these obstacles cannot bepenetrated by the wave. The future time T(x, y) of the wave is nowassigned to each point (x, y) in the space. T(x, y)=0 applies for pointswithin the target, and T(x, y)=∞ applies for points which cannot bereached, for example points in obstacles.

If F(x, y)=1 is selected for all points (x, y) which do not lie in anobstacle, the future time thus corresponds precisely to the Euclideanlength of the shortest path, that is to say the actual distance orEuclidean distance as shown in FIG. 2 a. The future times thuscorrespond to the sought potential. The potential thus calculated, whichcorresponds to the actual distances, that is to say the Euclideandistances, will be referred to hereinafter as the Euclidean potential,in contrast to the Manhattan potential, which is based on a 1-metric,that is to say a calculation of distance along the axes of symmetry ofthe cellular automata, in other words a Manhattan metric or 1-metric.

If, as illustrated in FIG. 2 b, an alternative F(x, y)>0 is selected,the specific future times and therefore distances thus correspond toanother weighting of the distances, that is to say any metric other thanthe natural weighting, that is to say the Euclidean metric. According tothe present approach, future times always correspond to distances, seealso the section on weighting of distances and selection of the metric.

A location-dependent weighting of distances is possible by selection ofthe propagation speed F(x, y), as illustrated in FIG. 2 b. If a smallerpropagation speed is selected in a specific area, the wave thuspropagates there more slowly. Points in the corresponding areas arereached later, since the wave covers shorter distances in the sameperiod of time. Distances in these areas are thus weighted more heavily.The shortest paths generally try to avoid these areas and therefore thepeople or particles also avoid these areas since they move in thedirection of the shortest path and thus follow this path. The directionof the shortest path in each point can be determined in each case bydetermining the gradient, that is to say the direction of the greatestchange in potential See also the section on determining the direction ofthe shortest path and motion methods. If a person were to move in thedirection of the greatest change in potential at a locally differentspeed F(x, y), that is to say at precisely the wave propagation speed,he would reach the target more quickly than on all other paths.Generally however, the speed of the person does not correspond to thepropagation speed of the wave F(x, y), even though both can vary locallyat the same time. The propagation speed of the wave F(x, y) is merely anauxiliary quantity in this context and is inversely proportional to theweighting of the distances, that is to say the metric. It does notcoincide with the actual speed of objects or people. For example, aperson thus moves approximately just as fast over grass and pavedsurfaces. Generally however, the person would try to avoid the grass,and therefore distances over this would be weighted more heavily. Thiswould imply a slower propagation speed F(x, y) of the wave propagationin order to determine the wave future time or the potential T(x, y). InFIG. 2 b for example, the lower left area could correspond to grass. Theactual speeds of the person would not be variable however, and would beconstant in all areas.

F(x, y) thus does not coincide with the speed of the person, but merelywith the preference for specific territories or other conditions.

FIG. 3 shows a hexagonal cell grid with an approximated Euclideanpotential. The considered cellular state automaton consists of a regulargrid with hexagonal cells, over which the considered particles or peoplemove in discrete time steps. As described before, a potential isassigned to each cell. A cell may or may not be occupied either by aperson or particle. The particles each move in discrete time steps tothe next cell, wherein the direction of motion is determined by thepotential of the adjacent cell. If more than one particle is considered,the path determination thus depends on those in the cells locatedadjacently.

FIG. 3 shows a schematic view of the proposed device in the example of acellular state automaton with hexagonal cells when considering theEuclidean metric, that is to say when considering actual distances. Inthe cells, the shortest distance of the centre point determined by meansof a fast-marching algorithm is provided. This potential forms the basisfor the path search. In conventional potential-based motion methods, ineach step the respective adjacent cell with the smallest potentialstarting from the current position is selected, and with a random pathsearch this adjacent cell is provided with a greater probability. Evenwhen using these conventional motion methods in combination with themethods implemented in this invention for calculating the underlyingpotentials for the purpose of target finding, much better results areobtained, more specifically illustrated as “path without correction” inFIG. 3, than with use of the Manhattan potentials used in conventionalsimulators of flows of people and objects. The latter lead primarily toa multiplicity of possible paths. However, if merely the local potentialminimums are considered, deviations from an ideal path, illustrated inFIG. 3 as the “shortest path”, are sometimes large even with use of themethods used here for calculating potential if the path “path withoutcorrection” in FIG. 3 is considered.

An advantageous implementation of a direction-based correction for aconventional motion method will be considered hereinafter, wherein thenext cell for the motion is selected merely on the basis of thepotential minimum, which corresponds to an approach of zero order. Anapproach of first order is selected for a direction-based correction.For example, there is a restriction to purely Euclidean potentials, thatis to say (F(x, y)=1 outside obstacles. An extension for arbitrarypotentials, that is to say arbitrary directions of distances or any F(x,y) outside obstacles is possible.

For each step, the direction of the shortest path is first determined,for example the direction of the gradient, that is to say the line“direction to the target” starting from point P0 in FIG. 3. Based onthis, the deviation n_(Δ) at right angles to the direction of theshortest path and the tangential deviation t_(Δ) in the direction of theshortest path are calculated for each cell which can be entered from thecurrent cell. The path from P0 to P1 is compared to the direct path“direction to the target” (line d). The tangential deviation n_(Δ) isthe path length P1S_(A). The tangential deviation t_(Δ) is the pathlength S_(A)S_(B). The point S_(A) is the intersection of theperpendiculars on line d by P1 with line d. The point S_(B) is the pointof intersection of the circular line with the centre point P0 and theradius P0P1 with the line d, that is to say the line of the direction tothe target. The deviations n_(Δ) are provided with a sign to determinethe direction of the deviation.

Instead of reducing the motion merely to the adjacent cell with thesmallest potential value, the two adjacent cells to the left and rightof the smallest potential value are additionally considered. From thesethree candidates, the deviations n_(Δ) at right angles to the directionof the greatest change in potential are determined. In addition, the sumof all deviations n_(Δ) from the previous step N_(Δ) is determined. In amemory-saving implementation, merely the sum is stored so that a storageof the individual deviations is omitted. The cell is now selected fromthe three potential candidates as the next cell on the path, andtherefore the absolute value of the sum of all previous steps of theperson plus the deviation for this step is minimal. If the cell to beselected is not the neighbor with the smallest potential, the potentialof the cell to be selected is reduced, merely for this person or theparticle in this step, until its potential values lies below the valueof the smallest potential. For example, this may be achieved bysubtracting the difference in the potentials plus a small number fromthe potential of the cell to be selected. The original method, whichmerely considers the potentials of the adjacent cell, which conventionalsimulation of flows of people use, can thus be retained. No furthermodifications of the conventional method are required, and for exampleother people can thus be considered by means of people repulsionpotentials.

The path determined using the device according to the invention is the“path with correction” b in FIG. 3. Owing to the restrictions of themotion through the grid, the length of the path b is greater than thedirect connection. At a predefined speed, a particle requires longer toreach the target than is to be expected with free motion. This is atypical problem of devices for the grid-based simulation of flows ofobjects and people.

However, according to the numerical solution of an eikonal equation, thevalues for the future times and the potential lie merely in the gridpoints of the underlying grid. That is to say in the cell centre pointsin our case. By means of interpolation however, the gradient can also beobtained using the device according to the invention. A schematic viewcan be found in FIG. 3. An area is spanned locally by linearinterpolation of the points P0, P1 and P2, which area passes through thethree points. With the aid of this area, the gradient/direction of thestrongest change can be determined locally in each point of the triangleformed by P0, P1 and P2, as illustrated in FIG. 3. The solution proposedby way of example in this instance corresponds to an interpolation offirst order of the potential for determining the gradient. Any otherapproaches for the approximate determination of the gradient arepossible however. In principle, any number of values and grid points canbe consulted in the approach developed in this instance in order todetermine the local direction of the greatest changes by means ofinterpolation.

FIG. 4 is a view of the average speed as a function of the direction oftravel and motion correction, more specifically speed correction. Thex-axis shows the direction of motion of the particles in degrees, andthe y-axis shows the average speed of particles in meters per second.FIG. 4 shows the average speed for a path of 40 m with a speed of travelof 1.34 m/s per particle for different directions of travel (in degrees)and corrections. The angular dependence of the direction of travel orthe grid dependence is shown very clearly with poor or no correction.

The tangential deviations t_(Δ) from the ideal path calculated in eachstep can be used to correct speed. If the sum of all deviations t_(Δ) ofall previous steps of this person or this particle exceeds an integralmultiple of the grid distance, the particle or person will thus begranted an additional step. The effective speed of the particle orperson is increased locally in terms of time. This corrections allowseffective speeds, as illustrated in FIG. 4. These effective speedsapproximate the expected journey times for a given path, represented bythe curve a in FIG. 4, much better than without correction, representedby the curve c in FIG. 4, or with use of known corrections, representedby the curve b in FIG. 4. For example, conventional corrections are therecognition of staggered steps.

In the presented advantageous memory-saving implementation of thismethod, merely the sum of all deviations n_(Δ) as well as the sum of alldeviations t_(Δ) has to be stored. In each time step, the correspondingcurrent deviations nΔ and tΔ are added together after selection of themove. Owing to the minimal number of variables to be calculated, theproposed device is also advantageous in terms of computationalintensity.

The correction device considered by way of example takes into accountthe sum of all deviations n_(Δ) and t_(Δ) in the past of each particle.Alternative approaches are also possible. If the particle is pushed toofar from its original path, for example by interaction with otherparticles, or if the particle finds itself in a situation in which thepath cannot actually be freely selected, for example in a dense crowd,it is appropriate to reinitialize the sum of all deviations, that is tosay to set to 0.

FIG. 5 shows a schematic view of the generation of a motion of particlesby means of a device according to the invention.

According to FIG. 5, the following steps are carried out in a deviceaccording to the invention. In a step S1, one proceeds similarly toconventional algorithms. In a step S2, the direction R of the shortestpath is determined. In a step S3, an adjacent cell Z_(M) with thesmallest potential value is established. In a step S4, the adjacentcells to the left Z_(L) and to the right Z_(R) of the cell Z_(M) aredetermined. In a step S5, the distances n_(Δ)(Z_(L)), n_(Δ)(Z_(M)) andn_(Δ)(Z_(R)) at right angles to the shortest path in the cells Z_(L),Z_(R), Z_(M) are determined. In a step S6, two conditions are set:

N _(Δ) +n _(Δ)(Z _(M))<N _(Δ) +n _(Δ)(Z _(L)) and N _(Δ) +n _(Δ)(Z_(M))<N _(Δ) +n _(Δ)(Z _(R))

If neither condition is met, the following inequality is examined in astep S7:

N _(Δ) +n _(Δ)(Z _(L))<N _(Δ) +n _(Δ)(Z _(R))

If the inequality in step 7 is met, a step S8 is performed. In the stepS8, the potential in Z_(L) is corrected merely for this particle and forthis step by the formula P(Z_(L))=P(Z_(M))−0.00001. If the inequality instep 7 is not met, a step S9 is performed. In the step S9, the potentialin Z_(R) is corrected merely for this particle and for this step by theformula P(Z_(R))=P(Z_(M))−0.00001. Step S10 follows the steps S8 and S9.The step S10 is also performed if, in step S6, the two equations aremet. In the step S10, the particles move similarly to the conventionalalgorithms. In a step S11, the sum of the deviations at right angles tothe shortest path N_(Δ)=N_(Δ)+n_(Δ)(Z) and parallel to the shortest pathT_(Δ)=T_(Δ)+t_(Δ)(Z) is stored. In a step S12, an extra step isperformed if T_(Δ) exceeds an integral multiple of the cell distances.All steps S1 to S12 represent a modified course of motion for each stepof each particle or each person. The steps S2 to s11 provide a directioncorrection. The steps S11 and S12 provide a speed correction.

FIG. 6 shows a comparison of conventional path determination and pathdetermination according to the present invention.

FIG. 6 shows a comparison of the different model-based methods for pathdetermination for a cellular state automaton with hexagonal symmetry.FIG. 6 a shows a Manhattan potential, that is to say the use ofDijkstra's algorithm with correction in the case of unobstructed view;FIG. 6 b shows a Euclidean potential and the use of a fast-marchingalgorithm without correction; FIG. 6 c shows the use of a Euclideanpotential with use of a fast-marching algorithm with the correctionaccording to the invention.

FIG. 6 a shows the unclear and unrealistic behavior of flows of objectsand people on the basis of Dijkstra's approach, which provides anunrealistically large number of possibilities of the motions.

Generally, the device according to the invention can also be implementedwithout corrections in terms of the motion directions and speeds. If, inexisting devices for simulating flows of objects and people, merely themethods for calculating the target potential are exchanged, much bettermotion patterns are provided than with use of a conventional Dijkstra'salgorithm. For example, there are much fewer bottlenecks at corners, asis illustrated for example in FIG. 6 b. Merely a minimal modification ofthe existing simulation device is necessary. Generally, only thefunction for potential calculation has to be replaced.

Furthermore, the device according to the invention allows real traveltimes of people to be approximated as precisely as possible. Thiscorrection is detached from potential. For example, it can also be usedin the event of an unobstructed view, since in this case the Euclideandistance can be determined directly.

A substantially more realistic space-time dynamic is provided, asillustrated in FIGS. 6 b and 6 c, since the motions are based on anapproximation of the actual distance weighting. Conventional simulatorsof flows of people and objects determine distances along thediscretization directions predefined intrinsically by the method, forexample along the directions of symmetry of the cells in cellular stateautomata. The quality of the motions in the method presented here isbased on the shortest paths with respect to arbitrary distanceweightings, that is to say in particular the Euclidean distanceweighting, and is merely limited by the discretization accuracy of thefast-marching method. The considerably realistic behavior of the peopleor particles simulating these people leads to a significant increase inthe validity of the simulators of flows of objects and people accordingto the invention, simultaneously with only a minimally greatercomputational effort.

FIG. 6 illustrates the comparison of different methods of path searchingin cellular state automata. The topology shows the people source on theleft and the respective target on the right. The direct path is blockedby an obstacle.

When using a flood-based path search by means of Dijkstra's algorithm,the people move too steeply towards the wall. They move around thecorner practically along the wall. This results in a bottleneck, asillustrated in FIG. 6 a. Not until after the obstacle is a correction orcontrol based on view possible, alternatively the people would be caughtbefore the wall. The same method with a Euclidean metric based on thecalculation by means of the eikonal equation, that is to say wavepropagation, leads to flatter angles and thus to no bottlenecks, asillustrated in FIG. 6 b. If, in addition, the proposed correction is nowtaken into account, the simulation of a flow of people demonstratesrealistic behavior: the people follow the shortest paths both in frontof and also after the obstacle, as illustrated in FIG. 6 c. Theadvantage of the simulator of flows of people proposed in accordancewith the invention is clearly visible.

FIG. 7 shows two embodiments of motions with different distanceweightings. FIG. 7 shows intelligent people flows over areas withdifferent preference, that is to say weighting. In FIG. 7 a, dark areasare avoided, and in FIG. 7 b light areas are avoided.

The device according to the invention enables a realistic path search.Many problems of conventional methods, which in many cases demonstratean unrealistic behavior of the flows of people and objects, are avoided.In particular, the proposed device allows the implementation of acertain intelligence of the pedestrians. It is thus possible toimplement preference for a specific territory, for example the avoidanceof roads or a dense crowd. Such territories are basically only enteredif they cannot be avoided, for example if a target is on the other sideof the road, the path over this territory being kept as short aspossible. This is illustrated in FIG. 7 a. This realistic behavior isimportant in particular if the free areas to be considered are large andthe expected densities of people are low, that is to say for examplewhen optimizing the design of shopping centers or when consideringcomplex spaces, partly covered by buildings.

FIG. 7 illustrates a further example formed on the basis of a potentialbased on distances with different weighting. In each case the personsource is located in the bottom left corner. The target of the person isin the top right corner. Depending on the weighting of the distances,areas are avoided or preferred. In FIG. 7 a a movement over the upperand lower areas is preferred, whereas in FIG. 7 b movement in the middlearea is preferred. In the first case, F(x, y) is greater over the upperand lower areas; in the second case it is greater over the middle area.In both cases the pedestrians demonstrate intelligent behavior and movepredominantly over the preferred areas and try to keep paths over theother areas as short as possible.

The above examples illustrate that it is possible to easily determinewhich elements of the present invention will be used on the basis of thebehavior of the particles or simulated people. This is possible as soonas there is access to the people data, for example in the form of avisualization or computer animation or in the form of calculationtables. Such information is generally provided, since it represents thebasic result of a simulation of a flow of people. Evaluations of thesimulation for the planning of an evacuation or for the design of escapeplans are based on this data.

FIG. 8 shows an exemplary embodiment of a simulation device or computerdevice according to the invention.

A computer device 9 may be formed as a simulation device I or generatesa motion of particles 3, which for example may be metal balls. Thesimulation device I forms a spatial region, wherein a cell grid 5divides the area into cells. Each cell is assigned a total potentialwhich can change over time. Particles 3, for example metal balls, arefirst positioned at a starting time on the cell grid 5. A number of n=50balls for example may correspond to the number of detected people. Bymeans of a control device 7, total potential values variable over timecan be assigned to the cells. For example, an electromagnet may beassigned to each cell, the magnetic force of which electromagnet isadjustable by means of the control device 7. The control device 7 canset a respective potential by means of a current through anelectromagnet. At a starting time Ts, the potentials are activated bymeans of the control device 7, the balls move starting from a respectivestarting cell S, in each case past other balls and obstacles H towardsthe target Z. At an end time Te, all balls may have reached theirtargets Z. To visualize and/or detect the motion of the balls, a seconddetection device 1, for example a camera, may be used. Theinformation—this may be the motion directions of particles 3—of thesecond detection device 1 can be used in a computer device 9 tocalculate respective particle potentials. The information of the seconddetection device 1 may also be evaluated in an evaluation device 11. Forexample, a particle density in the cell grid 5 can be detected andevaluated. The evaluation device 11 can emit control signals to acentral controller 13 for controlling building elements 15, for exampledoors or signs. The simulation device I may also be copied by a computerdevice 9 for example. The simulation device I is suitable in particularfor a simulation of flows of people, for example in buildings. The modelof the simulation device I according to the invention can be transferredto a computer device using a corresponding model. That is to say, thesimulation device I can also be copied by a computer. Such an embodimentis also included in the scope of protection of this application.

FIG. 9 shows an exemplary embodiment of a method according to theinvention.

In a step S1, a simulation device (I) with a spatial region superimposedby a cell grid (5) is provided, wherein each cell takes on variousoccupation and total potential states which are adjusted by means of acontrol device (7) and a computer device (9), wherein each cell isassigned a target potential determining how particles (3) are attractedto a target (Z), and an obstacle potential is assigned determining howparticles (3) are repelled by an obstacle (H), and wherein each particle(3) is assigned a particle potential, wherein a total potential in acell is made up of the values of the target potential and the obstaclepotential in the cell and the particle potentials of particles (3),detected by means of a second detection device, in cells adjacent to thecell. In a step S2, positions of people at a starting time over aspatial region to be monitored are detected by means of a firstdetection device (0) and metal balls (3) are positioned accordingly atrespective starting cells (S), wherein the metal balls (3) then eachchange from a cell into an adjacent cell having a least total potential;

In a step S3, the positions of the metal balls (3) are detected by meansof the second detection device (1). In a step S4, the total potentialstates are updated by means of the second detection device (1), thecomputer device (9) and the control device (7), wherein, starting fromthe target (Z) to each cell, the target potential for each cell iscalculated by means of a computer device (9) using a length of ashortest distance from the target (Z) to a respective cell centre point.In a step S5, the motions of the actual people (3) are controlled incase of forecast critical situations which were detected in advance bymeans of the computer device (9) or the simulation device (I). Forexample, a critical situation may be a bottleneck of people, which forexample is relieved by opening an additional passage (15) by means of acentral controller (13).

1-17. (canceled)
 18. A system for controlling motions of a multiplicityof particles in a spatial region having at least one target and at leastone obstacle, the system comprising: a first detection device fordetecting positions of the particles at a starting time; a computerdevice configured to predict a future path of the particles, wherein acell grid is superimposed on the region and each cell takes on variousoccupation and total potential states, and each cell is assigned atarget potential determining how particles are attracted to the at leastone target, and an obstacle potential is assigned determining howparticles are repelled by an obstacle, and wherein each particle isassigned a particle potential, wherein a total potential in a cell ismade up of the values of the target potential and the obstacle potentialin the cell and the particle potentials of particles in cells adjacentto the cell, and particles each change from a cell into an adjacent cellhaving a least total potential, and additionally, starting from a targetto each cell, the target potential for each cell has been calculatedusing a length of a shortest future path of a particle to the target ofa respective cell center point; and a central controller for controllingthe motions of the particles in case of a forecast critical situation.19. The system according to claim 18, wherein said computer device isconfigured for calculating the target potential by describing the targetas a curve of any shape, starting from the curve considering apropagation of a wave front, described by way of the curve, whereinvectors of a speed of the propagation F(x,y) are selected at rightangles to the wave front in each instance, and by calculating a futuretime T(x,y) of the wave front for each point (x,y) in the space, whereinthe target potential in the respective point (x,y) is calculated asdirectly proportional to the future time T(x,y) of the wave front in therespective point (x,y).
 20. The system according to claim 19, whereinthe propagation of the wave front is described mathematically by aneikonal equation:F(x,y)²[(δ_(x) T(x,y))²′+(δ_(y) T(x,y))²]=1.
 21. The system according toclaim 18, wherein said computer system is configured for selecting aplurality of spatially varying propagation speeds F(x,y)>0 for eachpoint (x,y) of the wave front instead of a speed of the propagationF(x,y) of the wave front, wherein a distance weighting occurs as aresult, which is location-dependent, and wherein the propagation speedF(x, y) is selected inversely proportional to the distance weighting.22. The system according to claim 18, wherein said computer devicelocally calculates a direction of a greatest change in magnitude of thetarget potential as the direction of the shortest path to the target,and based on the information thus obtained approximates a realisticmotion along the shortest path over the cell grid by way of a directioncorrection.
 23. The system according to claim 22, configured for:considering an adjacent cell with a smallest target potential value andadditionally two adjacent cells to the left and right of the adjacentcell with the smallest target potential value for direction correctionstarting from a current cell; establishing for each of the threeadjacent cells a normal deviation nΔ at right angles to the direction ofthe shortest path, starting from the local direction of the shortestpath of a cell center point of the current cell, a normal deviation nΔhaving a direction-dependent sign in each case; establishing a sum NΔ ofall normal deviations nΔ from the previous steps of an respectiveparticle; and selecting the adjacent cell acting as the next cell forthe particle in such a way that the absolute value of the sum NΔ of allprevious steps of the particle, including the normal deviation nΔ forthis step, is minimal, with the direction correction occurring as aresult of the selection.
 24. The system according to claim 23, whichcomprises a control device which, if the selected adjacent cell is notthe adjacent cell with the smallest target potential value, decreasesthe target potential of the selected adjacent cell until a value of thetarget potential is less than the smallest target potential value. 25.The system according to claim 18, wherein a speed correction for amomentary particle speed takes place by means of known previousdeviations from a shortest path.
 26. The system according to claim 25,wherein: a direction of a greatest change in the target potentiallocally determines a direction of the shortest path to the target; andwherein for speed correction starting from the local direction of theshortest path of a cell center point of a current cell, a tangentialdeviation tΔ in the direction of the shortest path is established forany step for each cell that is entered next from the current cell; a sumTΔ of all tangential deviations tΔ of all previous steps of a currentparticle is established; and an additional step for the particle isgranted by said control device if the sum TΔ of all tangentialdeviations tΔ of all previous steps for the particle is greater than anintegral multiple of a cell center point distance, wherein an effectivespeed of the particle is thus increased locally in terms of time and istherefore corrected.
 27. The system according to claim 23, wherein saidcontrol device is configure to set a sum NΔ of the normal deviations orthe sum TΔ of the tangential deviations to zero if the particle ispushed too far from its original path or if the particle cannot freelyselect its path.
 28. The system according to claim 22, wherein saidcontrol device is further configured, starting from the targetpotentials of three cell center points, to determine locally thedirection of the greatest change in the target potential byinterpolating each point of a triangle formed by three cell centerpoints.
 29. The system according to claim 18, wherein said computerdevice is configured to: determine locally a direction of a greatestchange in the target potential, which is a direction of the shortestpath to the target; and determine a current shortest path for a particleby way of a weighted averaging of greatest changes to the targetpotential of the shortest path of the particle in previous cells. 30.The system according to claim 18, wherein a path selection of theparticles is random-based and said computer device is configured tocalculate probabilities of individual cells on the basis of the totalpotential and the information regarding the direction of the shortestpath.
 31. The system according to claim 18, wherein said centralcontroller is configured for controlling elements of a building.
 32. Thesystem according to claim 31, wherein the elements of the building areselected from the group consisting of doors, windows, signs,loudspeakers, lifts, escalators, and lights.
 33. The system according toclaim 18, wherein the particles represent persons.
 34. A method ofcontrolling motions of a multiplicity of particles in a spatial regionhaving at least one target and at least one obstacle, the method whichcomprises: detecting positions of the particles at a starting time;predicting a future path search of the particles, wherein the region hasbeen superimposed by a cell grid and each cell takes on variousoccupation states and total potential states, and each cell is assigneda target potential determining how particles are attracted to a target,and an obstacle potential is assigned determining how particles arerepelled by an obstacle, and wherein each particle is assigned aparticle potential, wherein a total potential in a cell is made up ofthe values of the target potential and the obstacle potential in thecell and the particle potentials of particles in cells adjacent to thecell, and particles each change from a cell into an adjacent cell havinga least total potential, and additionally, starting from a target toeach cell, the target potential for each cell has been calculated usinga length of a shortest distance from the target to a respective cellcenter point; and controlling the motions of the particles in case offorecast critical situations.